Soliton Scattering by Impurities. An Analytical Approach to Interference Effects

Abstract

We have studied analytically the soliton scattering by point and finite-size inhomogeneities on the basis of the perturbed sine-Gordon and Korteweg-de Vries equations. The most remarkable feature of such scattering is interference effects caused by the resonant emission of solitons. These effects may be described by a reflection coefficient which is calculated by means of soliton perturbation theory, the intensity of the inhomogeneities being the small perturbation parameter. Our results are applied to the theory of long Josephson junctions with installed inhomogeneities and to the theory of one-dimensional nonlinear atomic lattices with isotope-like point defects.